Looking forward to is correct and is often followed by a word ending in "ing" (but not necessarily). "I look forward to having dinner with you" or "I look forward to your visit". As previously stated, for + that which is (possibly) anticipated.
It's awkward but I did locate some uses of "for" following "forward" where forward is used as the adverb "in front of". One example, "I am looking behind me for the police and looking forward for traffic problems". However, it was noted that "ahead of" would be perhaps a better word to use in that sentence as opposed to "forward". Actually, as I think about it (and look at it in it's adverb form) I can see some other appropriate uses of "for". "I drove slowly forward for fear I might miss running over my husband". Meh, even there I think "in" might be better than "for".
Definition of forward (Entry 2 of 4)
: to or toward what is ahead or in front
from that time forward
moved slowly forward
Personally, I'm looking forward to being informed that I answered this question in accordance with the forum's rules and policies.